Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems

Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, and Sandro Vaienti

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Abstract

We develop and generalise the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical systems, in particular to sequential dynamical systems, given by uniformly expanding maps, and to a few classes of random dynamical systems. Some examples are presented and worked out in detail.

Résumé

Nous développons et généralisons la théorie des valeurs extrêmes pour des processus stochastiques non-stationnaires, en affaiblissant la condition de mélange uniforme qui avait été utilisée auparavant. Nous appliquons nos résultats à des systèmes dynamiques non autonomes, en particulier aux systèmes dynamiques séquentiels engendrés par des applications dilatantes et à une large classe de systèmes dynamiques aléatoires. Quelques exemples sont présentés et calculés en détail.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 53, Number 3 (2017), 1341-1370.

Dates
Received: 1 December 2015
Revised: 4 April 2016
Accepted: 6 April 2016
First available in Project Euclid: 21 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1500624044

Digital Object Identifier
doi:10.1214/16-AIHP757

Mathematical Reviews number (MathSciNet)
MR3689970

Zentralblatt MATH identifier
1375.37026

Subjects
Primary: 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 60G70: Extreme value theory; extremal processes 37B20: Notions of recurrence 37A25: Ergodicity, mixing, rates of mixing

Keywords
Non-stationarity Extreme value theory Hitting Times Sequential dynamical systems Random dynamical systems

Citation

Freitas, Ana Cristina Moreira; Freitas, Jorge Milhazes; Vaienti, Sandro. Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems. Ann. Inst. H. Poincaré Probab. Statist. 53 (2017), no. 3, 1341--1370. doi:10.1214/16-AIHP757. https://projecteuclid.org/euclid.aihp/1500624044


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